Air-powered machines and tools used for machining, and more specially air-powered grinders, have to be supplied with air under pressure for powering them and, after expansion in the motor, the air then has to be piped off to some point clear of the machine while at the same time dirt produced by grinding has to be aspirated. For this purpose, three separate flexible pipe connections are needed and, if such pipes are simply joined together with wires or tapes, they are likely to get in the way of the user of the machine in some way or other.